Geometry Module PDF
Geometry Module PDF
Geometry Module PDF
Types of Triangles
A Scalene Triangle has 3 sides of different lengths. Because the sides are of different lengths, the
angles must also be of different measures.
An Isosceles Triangle has 2 sides with the same length (i.e., congruent). Because two sides are
congruent, two angles must also be congruent.
An Equilateral Triangle has 3 equal sides (i.e., congruent). Because all 3 sides are congruent, all 3 angles
must also be congruent. This requires each angle to be 60⁰.
A Right Triangle is one that contains a 90⁰ angle. It may be scalene or isosceles, but cannot be
equilateral. Right triangles have sides that meet the requirements of the Pythagorean Theorem.
Polygons ‐ Basics
Basic Definitions
Polygon: a closed path of three or more line segments, where:
- no two sides with a common endpoint are collinear, and
- each segment is connected at its endpoints to exactly two other segments.
Side: a segment that is connected to other segments (which are also sides) to form a polygon.
Vertex: a point at the intersection of two sides of the polygon. (plural form: vertices)
Diagonal: a segment, from one vertex to another, which is not a side.
Concave: A polygon in which it is possible to draw a diagonal “outside” the polygon. (Notice the orange
diagonal drawn outside the polygon atright.) Concave polygons actually look like they have a “cave” in them.
Convex: A polygon in which it is not possible to draw a diagonal “outside” the polygon. (Notice that all of the
orange diagonals are inside the polygon at right.) Convex polygons appear more “rounded” and do not contain
“caves.”
Definitions of Quadrilaterals
Quadrilateral A polygon with 4 sides.
Kite A quadrilateral with two consecutive pairs of congruent sides, but with opposite sides not
congruent.
Trapezoid A quadrilateral with exactly one pair of parallel sides.
Isosceles Trapezoid A trapezoid with congruent legs.
Parallelogram A quadrilateral with both pairs of opposite sides parallel.
Rectangle A parallelogram with all angles congruent (i.e., right angles).
Rhombus A parallelogram with all sides congruent.
Square A quadrilateral with all sides congruent and all angles congruent.